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2006 Interpolation and the Interpretability Logic of PA
Evan Goris
Notre Dame J. Formal Logic 47(2): 179-195 (2006). DOI: 10.1305/ndjfl/1153858645

Abstract

In this paper we will be concerned with the interpretability logic of PA and in particular with the fact that this logic, which is denoted by ILM, does not have the interpolation property. An example for this fact seems to emerge from the fact that ILM cannot express Σ₁-ness. This suggests a way to extend the expressive power of interpretability logic, namely, by an additional operator for Σ₁-ness, which might give us a logic with the interpolation property. We will formulate this extension, give an axiomatization which is modally complete and arithmetically complete (although for proofs of these theorems we refer to an earlier paper), and investigate interpolation. We show that this logic still does not have the interpolation property.

Citation

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Evan Goris. "Interpolation and the Interpretability Logic of PA." Notre Dame J. Formal Logic 47 (2) 179 - 195, 2006. https://doi.org/10.1305/ndjfl/1153858645

Information

Published: 2006
First available in Project Euclid: 25 July 2006

zbMATH: 1114.03048
MathSciNet: MR2240618
Digital Object Identifier: 10.1305/ndjfl/1153858645

Subjects:
Primary: 03B45
Secondary: 03F30

Rights: Copyright © 2006 University of Notre Dame

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